Learn Russian: Друзья желали нам удачи в дороге. - Our friends wished us luck on the journey.

The verb желать (to wish) governs the Genitive case for the thing being wished. While direct objects normally take the Accusative in Russian, verbs expressing desire, seeking, or wishing usually require the Genitive.

Why use the imperfective желали rather than the perfective пожелали?

Using the imperfective желали emphasizes the ongoing process or the atmosphere of the farewell. It paints a picture of the friends standing around and expressing their good wishes over a period of time. The perfective пожелали would simply state the completed, one-time fact that the wish was made.

Why say в дороге instead of на дороге to mean 'on the journey'?

The phrase в дороге is used idiomatically to mean 'in transit', 'during the trip', or 'on the way'. If you said на дороге, it would mean literally being physically positioned on the surface of the street or road, like a parked car or a pothole.

The recipient of the wish is нам. Does желать always use the Dative case for the person being wished well?

Yes! The person receiving the wish acts as the indirect object, so they take the Dative case (нам). You can think of the grammar as literally giving a wish 'to' someone.